Q. 16 - Algebra 2

Question

Find the next four terms of each arithmetic sequence.

 31, 24, 17, …

Step-by-Step Solution

Answer

The next four terms of the arithmetic sequence are 10, 3, -4, -11.

Step 1. Given Information.

The given arithmetic sequence is 31, 24, 17, …

Step 2. Calculation .

A sequence is said to be arithmetic when the difference between the consecutive terms is always the same.

 

Here the difference between the first two terms is  $24-31=-7$

The difference between the next two terms is  $17-24=-7$

So, the common difference is -7.

 

The next term in the arithmetic sequence is $17-7=10$ 

The next term in the arithmetic sequence is  $10-7=3$

The next term in the arithmetic sequence is $3-7=-4$ 

The next term in the arithmetic sequence is  $-4-7=-11$

Step 3. Conclusion .

Hence, the next four terms of the arithmetic sequence are 10, 3, -4, -11.